Exam 4: Random Variables and Probability Distributions

Suppose $x$ is a random variable best described by a uniform probability distribution with $c = 5$ and $d = 11$ . Find the value of a that makes the following probability statement true: $P ( x \leq a ) = 1$ .

(Multiple Choice)

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Question 61

A machine is set to pump cleanser into a process at the rate of 9 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the interval 9.0 to 11.0 gallons per minute. Would you expect the machine to pump more than 10.90 gallons per minute?

(Multiple Choice)

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Question 62

Suppose $\mathrm { x }$ is a random variable best described by a uniform probability distribution with $\mathrm { c } = 3$ and $d = 7$ . Find the value of a that makes the following probability statement true: $P ( x \geq a ) = 0.6$ .

(Multiple Choice)

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Question 63

$\text { Compute } \frac { 7 ! } { 3 ! ( 7 - 3 ) ! }$

(Multiple Choice)

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Question 64

The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 8.5. Find the probability that exactly four accidents will occur on this stretch of road each of the next two months.

(Multiple Choice)

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Question 65

Given that x is a hypergeometric random variable with $N = 8 , n = 4 , \text { and } r = 3 :$ a. Display the probability distribution in tabular form. b. Find $P ( x \leq 2 )$

(Essay)

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Question 66

Suppose $x$ is a random variable best described by a uniform probability distribution with $c = 2$ and $d = 10$ . Find the value of a that makes the following probability statement true: $P ( 2.5 \leq x \leq a ) = 0.5$ .

(Multiple Choice)

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Question 67

The preventable monthly loss at a company has a normal distribution with a mean of $7800 standard deviation of $30. A new policy was put into place, and the preventable loss the next month was $7620. What inference can you make about the new policy?

(Multiple Choice)

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Question 68

The board of examiners that administers the real estate broker's examination in a certain state found that the mean score on the test was 513 and the standard deviation was 72. If the board wants to set the passing score so that only the best 80% of all applicants pass, what is the passing score? Assume that the scores are normally distributed.

(Essay)

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Question 69

Suppose a Poisson probability distribution with $\lambda = 8.3$ provides a good approximation of the distribution of a random variable $x$ . Find $\sigma$ for $x$ .

(Multiple Choice)

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Question 70

Use the standard normal distribution to find $P ( - 2.25 < z < 1.25 ) .$

(Multiple Choice)

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Question 71

The amount of soda a dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a mean of 12.30 ounces and a standard deviation of 0.20 ounce. Each can holds a maximum of 12.50 ounces of soda. Every can that has more than 12.50 ounces of soda poured into it Causes a spill and the can must go through a special cleaning process before it can be sold. What is the probability that a randomly selected can will need to go through this process?

(Multiple Choice)

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Question 72

A new drug is designed to reduce a person's blood pressure. Eighteen randomly selected hypertensive patients receive the new drug. Suppose the probability that a hypertensive patient's blood pressure drops if he or she is untreated is 0.5. Then what is the probability of observing 16 or more blood pressure drops in a random sample of 18 treated patients if the new drug is in fact ineffective in reducing blood pressure? Round to six decimal places.

(Essay)

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Question 73

The amount of soda a dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a standard deviation of 0.26 ounce. Every can that has more than 12.65 ounces of soda poured into it causes a spill and the can must go through a special cleaning process before it can be sold. What is the mean amount of soda the machine should dispense if the company wants to limit the percentage that must be cleaned because of spillage to 3%?

(Multiple Choice)

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Question 74

An alarm company reports that the number of alarms sent to their monitoring center from customers owning their system follow a Poisson distribution with $\lambda = 4.7$ alarms per year. Identify the mean and standard deviation for this distribution.

(Multiple Choice)

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Question 75

$\text { Use the standard normal distribution to find } P ( - 2.25 < z < 0 ) \text {. }$

(Multiple Choice)

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Question 76

The Fresh Oven Bakery knows that the number of pies it can sell varies from day to day. The owner believes that on 50% of the days she sells 100 pies. On another 25% of the days she sells 150 pies, and she sells 200 pies on the remaining 25% of the days. To make sure she has enough product, the owner bakes 200 pies each day at a cost of $2 each. Assume any pies that go unsold are thrown out at the end of the day. If she sells the pies for $5 each, find the probability distribution for her dailyProfit.

(Multiple Choice)

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Question 77

Suppose a uniform random variable can be used to describe the outcome of an experiment with outcomes ranging from 20 to 90. What is the probability that this experiment results in an outcome less than 30? Round to the nearest hundredth when necessary.

(Multiple Choice)

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Question 78

The hypergeometric random variable x counts the number of successes in the draw of 5 elements from a set of 10 elements containing 2 successes. List the possible values of $x$ .

(Short Answer)

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Question 79

The hypergeometric random variable x counts the number of successes in the draw of 3 elements from a set of 8 elements containing 4 successes. List the possible values of $x$ .

(Short Answer)

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Question 80

Showing 61 - 80 of 273

Suppose $x$ is a random variable best described by a uniform probability distribution with $c = 5$ and $d = 11$ . Find the value of a that makes the following probability statement true: $P ( x \leq a ) = 1$ .

Suppose $\mathrm { x }$ is a random variable best described by a uniform probability distribution with $\mathrm { c } = 3$ and $d = 7$ . Find the value of a that makes the following probability statement true: $P ( x \geq a ) = 0.6$ .

$\text { Compute } \frac { 7 ! } { 3 ! ( 7 - 3 ) ! }$

The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 8.5. Find the probability that exactly four accidents will occur on this stretch of road each of the next two months.

Given that x is a hypergeometric random variable with $N = 8 , n = 4 , \text { and } r = 3 :$ a. Display the probability distribution in tabular form. b. Find $P ( x \leq 2 )$

Suppose $x$ is a random variable best described by a uniform probability distribution with $c = 2$ and $d = 10$ . Find the value of a that makes the following probability statement true: $P ( 2.5 \leq x \leq a ) = 0.5$ .

The preventable monthly loss at a company has a normal distribution with a mean of $7800 standard deviation of $30. A new policy was put into place, and the preventable loss the next month was $7620. What inference can you make about the new policy?

Suppose a Poisson probability distribution with $\lambda = 8.3$ provides a good approximation of the distribution of a random variable $x$ . Find $\sigma$ for $x$ .

Use the standard normal distribution to find $P ( - 2.25 < z < 1.25 ) .$

An alarm company reports that the number of alarms sent to their monitoring center from customers owning their system follow a Poisson distribution with $\lambda = 4.7$ alarms per year. Identify the mean and standard deviation for this distribution.

$\text { Use the standard normal distribution to find } P ( - 2.25 < z < 0 ) \text {. }$

Suppose a uniform random variable can be used to describe the outcome of an experiment with outcomes ranging from 20 to 90. What is the probability that this experiment results in an outcome less than 30? Round to the nearest hundredth when necessary.

The hypergeometric random variable x counts the number of successes in the draw of 5 elements from a set of 10 elements containing 2 successes. List the possible values of $x$ .

The hypergeometric random variable x counts the number of successes in the draw of 3 elements from a set of 8 elements containing 4 successes. List the possible values of $x$ .

Statistics, Data, and Statistical Thinking

Methods for Describing Sets of Data

Probability

Sampling Distributions

Inferences Based on a Single Sample: Estimation With Confidence Intervals

Inferences Based on a Single Sample: 355 Tests of Hypotheses

Inferences Based on Two Samples: Confidence Intervals and Tests of Hypotheses

Design of Experiments and Analysis of Variance

Categorical Data Analysis

Simple Linear Regression

Multiple Regression and Model Building

Methods for Quality Improvement: Statistical Process Control Available on CD

Time Series: Descriptive Analyses, Models, and Forecasting Available on CD

Nonparametric Statistics Available on CD

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Exam 4: Random Variables and Probability Distributions

Suppose xxx is a random variable best described by a uniform probability distribution with c=5c = 5c=5 and d=11d = 11d=11 . Find the value of a that makes the following probability statement true: P(x≤a)=1P ( x \leq a ) = 1P(x≤a)=1 .

Suppose x\mathrm { x }x is a random variable best described by a uniform probability distribution with c=3\mathrm { c } = 3c=3 and d=7d = 7d=7 . Find the value of a that makes the following probability statement true: P(x≥a)=0.6P ( x \geq a ) = 0.6P(x≥a)=0.6 .

Compute 7!3!(7−3)!\text { Compute } \frac { 7 ! } { 3 ! ( 7 - 3 ) ! } Compute 3!(7−3)!7!​

The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 8.5. Find the probability that exactly four accidents will occur on this stretch of road each of the next two months.

Given that x is a hypergeometric random variable with N=8,n=4, and r=3:N = 8 , n = 4 , \text { and } r = 3 :N=8,n=4, and r=3: a. Display the probability distribution in tabular form. b. Find P(x≤2)P ( x \leq 2 )P(x≤2)

Suppose xxx is a random variable best described by a uniform probability distribution with c=2c = 2c=2 and d=10d = 10d=10 . Find the value of a that makes the following probability statement true: P(2.5≤x≤a)=0.5P ( 2.5 \leq x \leq a ) = 0.5P(2.5≤x≤a)=0.5 .

The preventable monthly loss at a company has a normal distribution with a mean of $7800 standard deviation of $30. A new policy was put into place, and the preventable loss the next month was $7620. What inference can you make about the new policy?

Suppose a Poisson probability distribution with λ=8.3\lambda = 8.3λ=8.3 provides a good approximation of the distribution of a random variable xxx . Find σ\sigmaσ for xxx .

Use the standard normal distribution to find P(−2.25<z<1.25).P ( - 2.25 < z < 1.25 ) .P(−2.25<z<1.25).

An alarm company reports that the number of alarms sent to their monitoring center from customers owning their system follow a Poisson distribution with λ=4.7\lambda = 4.7λ=4.7 alarms per year. Identify the mean and standard deviation for this distribution.

Use the standard normal distribution to find P(−2.25<z<0). \text { Use the standard normal distribution to find } P ( - 2.25 < z < 0 ) \text {. } Use the standard normal distribution to find P(−2.25<z<0).

Suppose a uniform random variable can be used to describe the outcome of an experiment with outcomes ranging from 20 to 90. What is the probability that this experiment results in an outcome less than 30? Round to the nearest hundredth when necessary.

The hypergeometric random variable x counts the number of successes in the draw of 5 elements from a set of 10 elements containing 2 successes. List the possible values of xxx .

The hypergeometric random variable x counts the number of successes in the draw of 3 elements from a set of 8 elements containing 4 successes. List the possible values of xxx .

Statistics, Data, and Statistical Thinking

Methods for Describing Sets of Data

Probability

Sampling Distributions

Inferences Based on a Single Sample: Estimation With Confidence Intervals

Inferences Based on a Single Sample: 355 Tests of Hypotheses

Inferences Based on Two Samples: Confidence Intervals and Tests of Hypotheses

Design of Experiments and Analysis of Variance

Categorical Data Analysis

Simple Linear Regression

Multiple Regression and Model Building

Methods for Quality Improvement: Statistical Process Control Available on CD

Time Series: Descriptive Analyses, Models, and Forecasting Available on CD

Nonparametric Statistics Available on CD

Filters

Suppose $x$ is a random variable best described by a uniform probability distribution with $c = 5$ and $d = 11$ . Find the value of a that makes the following probability statement true: $P ( x \leq a ) = 1$ .

Suppose $\mathrm { x }$ is a random variable best described by a uniform probability distribution with $\mathrm { c } = 3$ and $d = 7$ . Find the value of a that makes the following probability statement true: $P ( x \geq a ) = 0.6$ .

$\text { Compute } \frac { 7 ! } { 3 ! ( 7 - 3 ) ! }$

Given that x is a hypergeometric random variable with $N = 8 , n = 4 , \text { and } r = 3 :$ a. Display the probability distribution in tabular form. b. Find $P ( x \leq 2 )$

Suppose $x$ is a random variable best described by a uniform probability distribution with $c = 2$ and $d = 10$ . Find the value of a that makes the following probability statement true: $P ( 2.5 \leq x \leq a ) = 0.5$ .

Suppose a Poisson probability distribution with $\lambda = 8.3$ provides a good approximation of the distribution of a random variable $x$ . Find $\sigma$ for $x$ .

Use the standard normal distribution to find $P ( - 2.25 < z < 1.25 ) .$

An alarm company reports that the number of alarms sent to their monitoring center from customers owning their system follow a Poisson distribution with $\lambda = 4.7$ alarms per year. Identify the mean and standard deviation for this distribution.

$\text { Use the standard normal distribution to find } P ( - 2.25 < z < 0 ) \text {. }$

The hypergeometric random variable x counts the number of successes in the draw of 5 elements from a set of 10 elements containing 2 successes. List the possible values of $x$ .

The hypergeometric random variable x counts the number of successes in the draw of 3 elements from a set of 8 elements containing 4 successes. List the possible values of $x$ .